A study among the Piria Indians of Arizona investigated the relationship between a mother's diabetic status and the number of birth defects in her children. The results appear in the two-way table.

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses.
$\begin{array}{cccc}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ Almost no chance }& 96& 98& 194\\ \text{ Some chance but }\text{ probably not }& 426& 286& 712\\ \text{ A 50-50 chance }& 696& 720& 1416\\ \text{ A good chance }& 663& 758& 1421\\ \text{ Almost certain }& 486& 597& 1083\\ \text{ Total }& 2367& 2459& 4826\end{array}$
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find $P(C\mid M)$. Interpret this value in context.

The two-way table summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level.

$\text{Grade}\text{Eat in cafeteria}\begin{array}{lrrrrr}& 9\mathrm{th}& 10\mathrm{th}& 11\mathrm{th}& 12\mathrm{th}& \text{ Total }\\ \text{ Yes }& 130& 175& 122& 68& 495\\ \text{ No }& 18& 34& 88& 170& 310\\ \text{ Total }& 148& 209& 210& 238& 805\end{array}$

If you choose a student at random who eats regularly in the cafeteria, what is the probability that the student is a 10th-grader?

Given an sample of data set X which is normal-distributed to $N(\mu =240,\sigma )$, I want to find the ${\displaystyle 95\mathrm{\%}}$ confidence interval of ${\displaystyle max(\mu -200,0)}$. As the ${\displaystyle max(\mu -200,0)}$ cut the normal-distribution curve at the point of 200, the sample of ${\displaystyle max(\mu -200,0)}$ is not more normal distributed. Therefore what is a reasonable ${\displaystyle 95\mathrm{\%}}$ confidence interval?